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Nilpotent deformations of an arbitrary background spacetime are considered . Those are of the form $\bg_{\m\n}+ l_\m l_\n$ with $l^2=0$. The relationship between the Ricci tensor of the background metric and the Ricci tensor of the deformed metric is found exactly. It consists of two terms. one is essentially the Fierz-Pauli operator, and the other is new. When the background is flat, the Kerr-Schild family is recovered. Novel examples (even including some simple sources) for more general backgrounds are discussed., Comment: Latex 13 pages,comments added, title changed

Linear superposition of gravitational fields is shown to be possible for a large class of spacetimes, in some specific coordinates. Explicit examples are presented., Comment: 11 pages, LaTeX, more details given

Gravitational plane waves (when Ricci flat) belong to the VSI family. The achronym VSI stands for vanishing scalar invariants, meaning that all scalar invariants built out of Riemann tensor and its derivatives vanish, although the Riemann tensor itself does not. In the particular case of plane waves many interesting phenomena have been uncovered for strings propagating in this background. Here we comment on gravitons propagating in such a spacetime, which itself presumably consists of an Avogadro number of such gravitons., Comment: 17 pages, LaTeX

In this paper we introduce a method that supports the detection, identification and localization of lamps in a building, with the main goal of automatically feeding its energy model by means of Building Information Modeling (BIM) methods. The proposed method, thus, provides useful information to apply energy-saving strategies to reduce energy consumption in the building sector through the correct management of the lighting infrastructure. Based on the unique geometry and brightness of lamps and the use of only greyscale images, our methodology is able to obtain accurate results despite its low computational needs, resulting in near-real-time processing. The main novelty is that the focus of the candidate search is not over the entire image but instead only on a limited region that summarizes the specific characteristics of the lamp. The information obtained from our approach was used on the Green Building XML Schema to illustrate the automatic generation of BIM data from the results of the algorithm., Comment: 12 pages, 19 figures, journal

Computer vision is used in this work to detect lighting elements in buildings with the goal of improving the accuracy of previous methods to provide a precise inventory of the location and state of lamps. Using the framework developed in our previous works, we introduce two new modifications to enhance the system: first, a constraint on the orientation of the detected poses in the optimization methods for both the initial and the refined estimates based on the geometric information of the building information modelling (BIM) model; second, an additional reprojection error filtering step to discard the erroneous poses introduced with the orientation restrictions, keeping the identification and localization errors low while greatly increasing the number of detections. These~enhancements are tested in five different case studies with more than 30,000 images, with results showing improvements in the number of detections, the percentage of correct model and state identifications, and the distance between detections and reference positions

This paper introduces a complete method for the automatic detection, identification and localization of lighting elements in buildings, leveraging the available building information modeling (BIM) data of a building and feeding the BIM model with the new collected information, which is key for energy-saving strategies. The detection system is heavily improved from our previous work, with the following two main contributions: (i) a new refinement algorithm to provide a better detection rate and identification performance with comparable computational resources and (ii) a new plane estimation, filtering and projection step to leverage the BIM information earlier for lamps that are both hanging and embedded. The two modifications are thoroughly tested in five different case studies, yielding better results in terms of detection, identification and localization.

The axion is a long-postulated boson that can simultaneously solve two fundamental problems of modern physics: the charge-parity symmetry problem in the strong interaction and the enigma of dark matter. In this work we estimate, by means of Monte Carlo simulations, the sensitivity of the Dark-photons$\&$Axion-Like particles Interferometer (DALI), a new-generation Fabry-P\'erot haloscope proposed to probe axion dark matter in the 25-250 $\mu$eV band., Comment: As accepted by Symmetry

It is well-known that in unimodular gravity the cosmological constant is not sourced by a constant energy density, but rather appears as some sort of integration constant. In this work we try to flesh this out by studying in some detail a couple of examples, one from cosmology and the other from gravitational collapse., Comment: LaTeX, 17 pages, cosmetic changes

The axion is a hypothetical boson arising from the most natural solution to the problem of charge and parity symmetry in the strong nuclear force. Moreover, this pseudoscalar emerges as a dark matter candidate in a parameter space extending several decades in mass. The Dark-photons \& Axion-Like particles Interferometer (DALI) is a proposal to search for axion dark matter in a range that remains under-examined. Currently in a design and prototyping phase, this haloscope is a multilayer Fabry-P\'erot interferometer. A proof-of-principle experiment is performed to observe the resonance in a prototype. The test unveils a quality factor per open cavity of a few hundred over a bandwidth of the order of dozens of megahertz. The result elucidates a physics potential to find the, so far elusive, axion, in a sector which can simultaneously solve the symmetry problem in the strong interaction and the enigma of dark matter., Comment: 5 pages, 6 figures

In this paper we study the behavior of a scalar field coupled to gravitons on the Janis-Newman-Winicour background, which somewhat interpolates between Minkowski and Schwarzschild space-times. The most important physical effect we find is that there is a 17-dimensional position-dependent mass matrix YABpxq which happens to be non-diagonal in the basis in which the kinetic energy term is diagonal. There is a different basis with a mixing between the scalar field and the graviton trace in which the mass matrix is diagonal, but this basis fails to diagonalize the kinetic energy piece. This is at variance with what happens in the Standard Model with the quark mixing, and is of course due to the fact that the mass matrix here is position dependent and thus it does not commute with the kinetic energy operator, so that both operators cannot be diagonalized simultaneously., Comment: 22 pages, LaTeX

When implementing a non-linear constraint in quantum field theory by means of a Lagrange multiplier, $\l(x)$, it is often the case that quantum dynamics induce quadratic and even higher order terms in $\l(x)$, which then does not enforce the constraint anymore. This is illustrated in the case of Unimodular Gravity, where the constraint is that the metric tensor has to be unimodular ($g(x)\equiv \det\,g_{\m\n}(x)=-1$)., Comment: 12 pages, 2 figures. A change in the Acknowledgemwnts section

We discuss the discovery potential of the Dark-photons & Axion-Like particles Interferometer (DALI) in this letter. The apparatus, currently in a design and prototyping phase, will probe axion dark matter from the Teide Observatory, an environment protected from terrestrial microwave sources, reaching Dine--Fischler--Srednicki--Zhitnitsky-like axion sensitivity in the range 25--250 $\mu$eV of mass. The experimental approach shows a potential to probe dark sector photons of kinetic mixing strength in excess of several $10^{-16}$, and to establish new constraints to a stochastic gravitational wave background in its band. We identify different branches, including cosmology, stellar, and particle physics, where this next-generation halo-telescope may play a role in coming years., Comment: As accepted by PRD [8 pages, 5 figures + Supplemental Material 4 pages, 3 figures]. https://journals.aps.org/prd/accepted/1f074Q62Pa91023535875f66ca556bf86dda6f468

Unimodularity can be implemented in different ways. In this paper we consider only the formulation of Unimodular Gravity in which the unimodular metric is obtained out of an unrestricted one as $\g_{\m\n}=|g|^{-{1\over n}} g_{\m\n}$. This procedure induces an extra Weyl symmetry. Some physical implications of this symmetry on the conserved currents are discussed. Finally the results are illustrated for the Painlev\'e-Gullstrand extension of Schwarzschild spacetime., Comment: LateX, 19 pages, figure included, revised

The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of motion, assuming it to be spherically symmetric, not necessarily static. Even in the non-spherically symmetric case, we present a necessary condition for an algebraically generic spacetime to solve the corresponding equations of motion. Some examples of an application of said condition are explicitly worked out., Comment: 12 pages

This chapter provides an introduction to Unimodular Gravity both at the classical and quantum level, discussing the r\^ole it might play in the partial solution of the Cosmological Constant problem. The main objective of this work is to serve as a conceptual introduction to Unimodular gravity without disregarding computational detail. In that sense, techniques used at the research level are presented and applied in detail., Comment: 40 pages, Invited chapter for "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto, and I. L. Shapiro, Springer 2023). Minor typos corrected

In recent years the advance of chemical synthesis has made it possible to obtain \textquotedblleft naked\textquotedblright clusters of different transition metals. It is well known that cluster experiments allow studying the fundamental reactive behavior of catalytic materials in an environment that avoids the complications present in extended solid-phase research. In physicochemical terms, the question that arises is the chemical reduction of metallic clusters could be affected by the presence of H$_{_{2}}$ molecules, that is, by the probability of encounter that these small metal atomic agglomerates can have with these reducing species. Therefore, we consider the stochastic movement of $N$ molecules of hydrogen in a cubic box containing $M$ metallic atomic clusters in a confined region of the box. We use a Wiener process to simulate the stochastic process, with $\sigma$ given by the Maxwell-Boltzmann relationships, which enabled us to obtain an analytical expression for the probability density function. This expression is an exact expression, obtained under an original proposal outlined in this work, \textit{i.e.} obtained from considerations of \textit{mathematical rebounds}. On this basis, we obtained the probability of encounter for three different volumes, $0.1^{^{3}}$, $ 0.2^{^{3}} $ and $ 0.4^{^{3}} $ m$^{^{3}}$, at three different temperatures in each case, $293$, $373$ and $473$ K, for $ 10^{^{1}}\leq N \leq10^{^{10}}$, comparing the results with those obtained considering the distribution of the position as a Truncated Normal Distribution. Finally, we observe that the probability is significantly affected by the number $N$ of molecules and by the size of the box, not by the temperature., Comment: 17 pages, 6 figures, 2 tables, 2 appendix (with 9 tables each)

The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital (nonlinear) instability in appropriate periodic Sobolev spaces. The analysis is based on the well-posedness theory, the smoothness of the data-solution map, and an abstract result of instability of equilibria under nonlinear iterations. The resulting instability criterion is applied to two families of periodic waves. The first family consists of small amplitude waves with finite fundamental period which emerge from a local Hopf bifurcation around a critical value of the velocity. The second family comprises arbitrarily large period waves which arise from a homoclinic (global) bifurcation and tend to a limiting traveling pulse when their fundamental period tends to infinity. In the case of both families, the criterion is applied to conclude their orbital instability under the flow of the nonlinear viscous balance law in periodic Sobolev spaces with same period as the fundamental period of the wave., Comment: 28 pages. 4 figures

We have studied a lagrangian in which the Einstein-Hilbert term is deformed by the Weyl cube operator, which is the lowest-dimension operator that is non-vanishing on shell and appears as a two-loop counterterm. There is a tension between the Schwarzschild de Sitter (SdS) spacetime and this operator, which we study in some detail., Comment: 29 pages, expanded; references added

In this paper some techniques useful to perform quantum field theory computations in a covariant manner are reviewed. In particular the background field gauge, the zeta function regularization and the heat kernel approach are highlighted. Some detailed calculations of the Schwinger-de Witt coefficients of the small proper time expansion of the heat kernel are also repeated in detail. This work reports lectures given by Enrique \'Alvarez at the IFT-UAM-CSIC in Madrid., Comment: 96 pages, LaTeX, lecture notes given by Enrique \'Alvarez at the IFT-UAM-CSIC in Madrid. New section added. References added. Typos corrected

The divergences coming from a particular sector of gravitational fluctuations around a generic background in general theories of quadratic gravity are analyzed. They can be summarized in a particular type of scalar model, whose properties are analyzed., Comment: 23 pages. No figures. References and comments added

A hyperbolic model for diffusion, nonlinear transport (or advection) and production of a scalar quantity, is considered. The model is based on a constitutive law of Cattaneo-Maxwell type expressing non-Fickian diffusion by means of a relaxation time relation. The production or source term is assumed to be of logistic type. This paper studies the existence and spectral stability properties of spatially periodic traveling wave solutions to this system. It is shown that a family of subcharacteristic periodic waves emerges from a local Hopf bifurcation around a critical value of the wave speed. These waves have bounded fundamental period and small-amplitude. In addition, it is shown that these waves are spectrally unstable as solutions to the hyperbolic system. For that purpose, it is proved that the Floquet spectrum of the linearized operator around a wave can be approximated by a linear operator whose point spectrum intersects the unstable half plane of complex numbers with positive real part., Comment: 24 pages, 2 figures

It is claimed that in the unimodular gravity framework the observational fact of exponential expansion of the universe cannot be taken as evidence for the presence for a cosmological constant or similar quintessence., Comment: 17 pages

Several alternative formulations of the first order approach to unimodular gravity are presented. There is always a particular one such that it is {\em classically} equivalent to the second order formulation; this we call {\em educated}. It is often at variance with the {\em naive} approach, in which the lagrangian is taken as given exactly by the same expression as in the second order formulation; only the number and character of the independent variables changes. Namely, typically some of the momenta are now considered as coordinates. The ensuing Hamiltonians are thereby discussed and their physical differences pointed out., Comment: 28 pages

The full one-loop (scalar) effective action is computed for both hyperbolic and elliptic spacetimes., Comment: LaTeX, 13 pages, references added

We discuss the weight of vacuum energy in various contexts. First, we compute the vacuum energy for flat spacetimes of the form $\mathbb{T}^3 \times \mathbb{R}$, where $\mathbb{T}^3$ stands for a general 3-torus. We discover a quite simple relationship between energy at radius $R$ and energy at radius $\frac{l_s^2}{ R}$. Then we consider quantum gravity effects in the vacuum energy of a scalar field in $\mathbb{M}_3 \times S^1$ where $\mathbb{M}_3$ is a general curved spacetime, and the circle $S^1$ refers to a spacelike coordinate. We compute it for General Relativity and generic transverse {\em TDiff} theories. In the particular case of Unimodular Gravity vacuum energy does not gravitate., Comment: 32 pages. Minor corrections

This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a reaction function of monostable or Fisher-KPP type. Under suitable structural assumptions, it is shown that this class of equations underlies two families of periodic waves. The first family consists of small amplitude waves with finite fundamental period which emerge from a Hopf bifurcation around a critical value of the wave speed. The second family pertains to arbitrarily large period waves which arise from a homoclinic bifurcation and tend to a limiting traveling (homoclinic) pulse when their fundamental period tends to infinity. For both families, it is shown that the Floquet (continuous) spectrum of the linearization around the periodic waves intersects the unstable half plane of complex values with positive real part, a property known as spectral instability. For that purpose, in the case of small-amplitude waves it is proved that the spectrum of the linearized operator around the wave can be approximated by that of a constant coefficient operator around the zero solution and determined by a dispersion relation which intersects the unstable complex half plane. In the case of large period waves, we verify that the family satisfies the assumptions of the seminal result by Gardner (1997, J. Reine Angew. Math. 491, pp. 149-181) of convergence of periodic spectra in the infinite-period limit to that of the underlying homoclinic wave, which is unstable. A few examples are discussed., Comment: 46 pages, 18 figures. Key words: viscous balance laws, periodic traveling waves, Floquet spectrum, spectral instability

This paper is concerned with the structural stability of spherical horizons. By this we mean stability with respect to variations of the second member of the corresponding differential equations, corresponding to the inclusion of the contribution of operators quadratic in curvature. This we do both in the usual second order approach (in which the independent variable is the spacetime metric) and in the first order one (where the independent variables are the spacetime metric and the connection field). In second order, it is claimed that the generic solution in the asymptotic regime (large radius) can be matched not only with the usual solutions with horizons (like Schwarzschild-de Sitter) but also with a more generic (in the sense that it depends on more arbitrary parameters) horizonless family of solutions. It is however remarkable that these horizonless solutions are absent in the {\em restricted} (that is, when the background connection is the metric one) first order approach., Comment: 42 pages, references added

These are notes for a graduate course in quantum gravity planned at IFT-UAM/CSIC for the spring term of 2020, but delayed for an indefinite period of time (although a shortened version was given in the Escuela de Fisica (Institute of Physics) in the University of Costa Rica.). The aim of the course was to highlight the most important conceptual problems in the field and to summarize some of the most imaginative solutions to them that have been proposed in the literature. The course can best be characterized as idiosyncratic rather than encyclopedic., Comment: 73 pages; 7 figures. Lectures on quantum gravity. Small changes; references added

A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal isometry group is of maximal rank and the conformal Killing vectors in conformally flat coordinates are {\em exactly} the same as the ones of flat spacetime. In this work, a new concept of distance is introduced, the {\em conformal distance}, which transforms covariantly under all conformal isometries of the CF space. It is shown that precisely for CF spacetimes, an adequate power of the said conformal distance is a solution of the non-minimal d'Alembert equation., Comment: Minor changes and some clarifications added. Published version. 16 pages

The generalization of scale invariance when gravitational effects are considered is Weyl invariance, namely, invariance under (global or local) rescalings of the metric. In this work, we discuss in some details the implications of the fact that the value of the anomaly for the global Weyl invariant coupling of scalar fields to gravity is sensitive to the dynamics (or absence thereof) of the gravitational field., Comment: 24 pages, streamlined, some errata fixed

The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms, linearized Weyl rescalings, and conformal transformations., Comment: 24 pages

A definition of quasi-local energy in a gravitational field based upon its embedding into flat space is discussed. The outcome is not satisfactory from many points of view., Comment: 12 pages